%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV182+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:40 AM UTC 2025
% Result : Theorem 0.20s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV182+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:31:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(init_type, type, (
% 0.20/0.52 init: $i)).
% 0.20/0.52 tff(a_select2_type, type, (
% 0.20/0.52 a_select2: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_G_13_type, type, (
% 0.20/0.52 tptp_fun_G_13: $i)).
% 0.20/0.52 tff(rho_init_type, type, (
% 0.20/0.52 rho_init: $i)).
% 0.20/0.52 tff(leq_type, type, (
% 0.20/0.52 leq: ( $i * $i ) > $o)).
% 0.20/0.52 tff(n4_type, type, (
% 0.20/0.52 n4: $i)).
% 0.20/0.52 tff(n0_type, type, (
% 0.20/0.52 n0: $i)).
% 0.20/0.52 tff(sigma_init_type, type, (
% 0.20/0.52 sigma_init: $i)).
% 0.20/0.52 tff(gt_type, type, (
% 0.20/0.52 gt: ( $i * $i ) > $o)).
% 0.20/0.52 tff(loopcounter_type, type, (
% 0.20/0.52 loopcounter: $i)).
% 0.20/0.52 tff(mu_init_type, type, (
% 0.20/0.52 mu_init: $i)).
% 0.20/0.52 tff(a_select3_type, type, (
% 0.20/0.52 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.52 tff(center_init_type, type, (
% 0.20/0.52 center_init: $i)).
% 0.20/0.52 tff(q_init_type, type, (
% 0.20/0.52 q_init: $i)).
% 0.20/0.52 tff(n135299_type, type, (
% 0.20/0.52 n135299: $i)).
% 0.20/0.52 tff(n1_type, type, (
% 0.20/0.52 n1: $i)).
% 0.20/0.52 tff(pv76_type, type, (
% 0.20/0.52 pv76: $i)).
% 0.20/0.52 tff(tptp_float_0_001_type, type, (
% 0.20/0.52 tptp_float_0_001: $i)).
% 0.20/0.52 tff(succ_type, type, (
% 0.20/0.52 succ: $i > $i)).
% 0.20/0.52 tff(1,plain,
% 0.20/0.52 ((~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))) <=> (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 ((~(((((((leq(tptp_float_0_001, pv76) & leq(n1, loopcounter)) & ![A: $i] : ((leq(n0, A) & leq(A, n135299)) => ![B: $i] : ((leq(n0, B) & leq(B, n4)) => (a_select3(q_init, A, B) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, n4)) => (a_select3(center_init, C, n0) = init))) & (gt(loopcounter, n0) => ![D: $i] : ((leq(n0, D) & leq(D, n4)) => (a_select2(mu_init, D) = init)))) & (gt(loopcounter, n0) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(rho_init, E) = init)))) & (gt(loopcounter, n0) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(sigma_init, F) = init)))) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(rho_init, G) = init)))) <=> (~((~(leq(tptp_float_0_001, pv76) & leq(n1, loopcounter) & ![A: $i] : ((~(leq(n0, A) & leq(A, n135299))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(center_init, C, n0) = init)) & ((~gt(loopcounter, n0)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(mu_init, D) = init))) & ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) & ((~gt(loopcounter, n0)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigma_init, F) = init))))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(3,axiom,(~(((((((leq(tptp_float_0_001, pv76) & leq(n1, loopcounter)) & ![A: $i] : ((leq(n0, A) & leq(A, n135299)) => ![B: $i] : ((leq(n0, B) & leq(B, n4)) => (a_select3(q_init, A, B) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, n4)) => (a_select3(center_init, C, n0) = init))) & (gt(loopcounter, n0) => ![D: $i] : ((leq(n0, D) & leq(D, n4)) => (a_select2(mu_init, D) = init)))) & (gt(loopcounter, n0) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(rho_init, E) = init)))) & (gt(loopcounter, n0) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(sigma_init, F) = init)))) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(rho_init, G) = init)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cl5_nebula_init_0086')).
% 0.20/0.52 tff(4,plain,
% 0.20/0.52 (~((~(leq(tptp_float_0_001, pv76) & leq(n1, loopcounter) & ![A: $i] : ((~(leq(n0, A) & leq(A, n135299))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(center_init, C, n0) = init)) & ((~gt(loopcounter, n0)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(mu_init, D) = init))) & ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) & ((~gt(loopcounter, n0)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigma_init, F) = init))))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.52 tff(5,plain,
% 0.20/0.52 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.20/0.52 inference(or_elim,[status(thm)],[4])).
% 0.20/0.52 tff(6,plain,
% 0.20/0.52 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.52 tff(8,plain,
% 0.20/0.52 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.52 tff(9,plain,(
% 0.20/0.52 ~((~(leq(n0, G!13) & leq(G!13, n4))) | (a_select2(rho_init, G!13) = init))),
% 0.20/0.52 inference(skolemize,[status(sab)],[8])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (~(a_select2(rho_init, G!13) = init)),
% 0.20/0.52 inference(or_elim,[status(thm)],[9])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 (leq(n0, G!13) & leq(G!13, n4)),
% 0.20/0.52 inference(or_elim,[status(thm)],[9])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (leq(G!13, n4)),
% 0.20/0.52 inference(and_elim,[status(thm)],[11])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (leq(n0, G!13)),
% 0.20/0.52 inference(and_elim,[status(thm)],[11])).
% 0.20/0.52 tff(14,plain,
% 0.20/0.52 ((succ(n0) = n1) <=> (succ(n0) = n1)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(15,axiom,(succ(n0) = n1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_1')).
% 0.20/0.52 tff(16,plain,
% 0.20/0.52 (succ(n0) = n1),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 (leq(succ(n0), loopcounter) <=> leq(n1, loopcounter)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.52 tff(18,plain,
% 0.20/0.52 (leq(n1, loopcounter) <=> leq(succ(n0), loopcounter)),
% 0.20/0.52 inference(symmetry,[status(thm)],[17])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (leq(n1, loopcounter) <=> leq(n1, loopcounter)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 (leq(tptp_float_0_001, pv76) & leq(n1, loopcounter) & ![A: $i] : ((~(leq(n0, A) & leq(A, n135299))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(center_init, C, n0) = init)) & ((~gt(loopcounter, n0)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(mu_init, D) = init))) & ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) & ((~gt(loopcounter, n0)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigma_init, F) = init)))),
% 0.20/0.52 inference(or_elim,[status(thm)],[4])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 (leq(n1, loopcounter)),
% 0.20/0.52 inference(and_elim,[status(thm)],[20])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 (leq(n1, loopcounter)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.20/0.52 tff(23,plain,
% 0.20/0.52 (leq(succ(n0), loopcounter)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.52 tff(24,plain,
% 0.20/0.52 (^[X: $i, Y: $i] : refl(((~leq(succ(X), Y)) | gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (^[X: $i, Y: $i] : rewrite((leq(succ(X), Y) => gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 (![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.52 tff(29,axiom,(![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_gt')).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.52 tff(32,plain,(
% 0.20/0.52 ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.20/0.52 inference(skolemize,[status(sab)],[31])).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.52 tff(34,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(n0), loopcounter)) | gt(loopcounter, n0))) <=> ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(n0), loopcounter)) | gt(loopcounter, n0))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(n0), loopcounter)) | gt(loopcounter, n0))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(36,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(n0), loopcounter)) | gt(loopcounter, n0)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.52 tff(37,plain,
% 0.20/0.52 ((~leq(succ(n0), loopcounter)) | gt(loopcounter, n0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.20/0.52 tff(38,plain,
% 0.20/0.52 (gt(loopcounter, n0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[37, 23])).
% 0.20/0.52 tff(39,plain,
% 0.20/0.52 (((~gt(loopcounter, n0)) | ![E: $i] : ((a_select2(rho_init, E) = init) | (~leq(n0, E)) | (~leq(E, n4)))) <=> ((~gt(loopcounter, n0)) | ![E: $i] : ((a_select2(rho_init, E) = init) | (~leq(n0, E)) | (~leq(E, n4))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(40,plain,
% 0.20/0.52 (((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) <=> ((~gt(loopcounter, n0)) | ![E: $i] : ((a_select2(rho_init, E) = init) | (~leq(n0, E)) | (~leq(E, n4))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(41,plain,
% 0.20/0.52 (((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) <=> ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(42,plain,
% 0.20/0.52 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.20/0.52 inference(and_elim,[status(thm)],[20])).
% 0.20/0.52 tff(43,plain,
% 0.20/0.52 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.52 tff(44,plain,
% 0.20/0.52 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.20/0.52 tff(45,plain,
% 0.20/0.52 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.20/0.52 Proof display could not be completed: monotonicity rule is not handled
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------